A Dynamical Phyllotaxis Model to Determine Floral Organ Number

Abstract

How organisms determine particular organ numbers is a fundamental key to the development of precise body structures; however, the developmental mechanisms underlying organ-number determination are unclear. In many eudicot plants, the primordia of sepals and petals (the floral organs) first arise sequentially at the edge of a circular, undifferentiated region called the floral meristem, and later transition into a concentric arrangement called a whorl, which includes four or five organs. The properties controlling the transition to whorls comprising particular numbers of organs is little explored. We propose a development-based model of floral organ-number determination, improving upon earlier models of plant phyllotaxis that assumed two developmental processes: the sequential initiation of primordia in the least crowded space around the meristem and the constant growth of the tip of the stem. By introducing mutual repulsion among primordia into the growth process, we numerically and analytically show that the whorled arrangement emerges spontaneously from the sequential initiation of primordia. Moreover, by allowing the strength of the inhibition exerted by each primordium to decrease as the primordium ages, we show that pentamerous whorls, in which the angular and radial positions of the primordia are consistent with those observed in sepal and petal primordia in Silene coeli-rosa, Caryophyllaceae, become the dominant arrangement. The organ number within the outmost whorl, corresponding to the sepals, takes a value of four or five in a much wider parameter space than that in which it takes a value of six or seven. These results suggest that mutual repulsion among primordia during growth and a temporal decrease in the strength of the inhibition during initiation are required for the development of the tetramerous and pentamerous whorls common in eudicots.

Stochastic occurrence of trimery from pentamery in floral phyllotaxis of Anemone (Ranunculaceae)

“…These three positions were consistent with a continuous spiral having a constant divergence angle in the phyllotaxis. The model further suggests that the organ growth rate, which plays a central role in the transition between tetramerous and pentamerous whorls [4], also has a central role in biasing the frequency of trimerous whorls.…”

“…Following the earlier model for floral phyllotaxis, α represents the difference of inhibitory effect due to growth progression on pre-existing organs. The α can account for the change of the direction of auxin flux toward the inner tissue of primordia and/or primordial boundary establishment and the increase of primordial volume [4]. A position at the global energy minimum is expected to be the most frequently observed position, while a position at the local minima will correspond to the second or lower frequency ranks.…”

“…1a,b) can be caused by the size or growth speed of meristem [2,3], little is known about developmental mechanisms that determine the specific number of perianth organs. We previously improved phyllotaxis models by showing that tetramerous and pentamerous whorls emerge from spiral initiation of floral organ primordia, as observed in eudicot flower development, and that whorl emergence depends on the rate of organ growth independent of meristem properties [4]. Transitions between pentamerous and trimerous whorls (Fig.…”

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

“…produced by a developing primordium that would inhibit the initiation of nearby primordia, successfully recapitulating known phyllotactic patterns in the shoot apical meristem (Bernasconi, 1994;Meinhardt, 2004;Jönsson et al, 2005;Nikolaev et al, 2007;Hohm et al, 2010;Fujita et al, 2011), the number of floral organs (Kitazawa and Fujimoto, 2015), the regular spacing of root hairs (Meinhardt and Gierer, 1974), and the establishment of specific vascular patterns (Meinhardt, 1976).…”

Emergence of complex patterns in a higher-dimensional phyllotactic system

“…In particular, this accounts for the influence exerted by primordia other than the immediate adjacents on the position of formation of the newest. Several authors [5][6][7][8][9] (and references therein) exemplified this idea. Notably, Douady and Couder [10] applied it to the modified Hofmeister rule and presented a seminal study on quantitative and qualitative dynamical properties of their model.…”